Vector bundles on a K3 surface

TL;DR

This paper explores the properties of vector bundles on K3 surfaces, demonstrating algebraicity of Hodge cycles, rigidity of certain curves, and providing new descriptions of Fano threefolds, along with simplified moduli space constructions.

Contribution

It introduces novel insights into the structure of vector bundles on K3 surfaces, including algebraicity results and applications to Fano threefolds.

Findings

Proved algebraicity of specific Hodge cycles

Established rigidity of genus eleven curves

Provided new descriptions of Fano threefolds

Abstract

A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of Fano threefolds as applications. In the final section we discuss a simplified construction of moduli spaces.